Electrically-charged particle energy analyzers

ABSTRACT

A charged particle energy analyzer (FIG.  1 ) comprises a source of electrons  1  and inner and outer cylinders ( 2,3 ) arranged concentrically about a longitudinal axis (z—z). Electrical potential applied to the outer cylinder ( 3 ) creates an electrostatic field between the cylinders ( 2,3 ) defined by equipotentials which are symmetrical about the longitudinal axis z—z and increase linearly in the longitudinal direction and logarithmically in the radial direction. Electrons having different energies are focused by the electrostatic field at discrete positions spaced apart from each other in the longitudinal direction. Also described is a charged particle energy analyzer (FIG.  6 ) in which electrons having different energies are fcoused by the electrostatic field at discrete positions at a surface transverse to the longitudinal axis. Both analysers may operate in the second-order focusing mode.

FIELD OF THE INVENTION

This invention relates to charged particle energy analysers,particularly, though not exclusively, charged particle energy analysershaving the capability to analyse simultaneously charged particles havinga wide range of energies.

BACKGROUND OF THE INVENTION

In charged particle optical systems various devices are available foranalysing the spectrum of energies of beams of charged particles andthese devices have been comprehensively described in various works onthe subject of charged particle optics; see for example, “Principles ofElectron Optics” by P. H. Hawkes and E. Kasper (Academic Press, NewYork) 1989, and a paper by D. Roy and D. Tremblay, Rep Prog Phys. 53,1621 (1990). In many applications, such as Auger electron spectroscopyof surfaces, the range of energies of interest in a single spectrum cancover more than an order of magnitude. The conventional way of obtainingsuch a spectrum has been to scan through the energy range using a singledetector. A faster technique is to use a multidetector or series ofdetectors to cover an extended range of energies and then to scan thecomplete range of the spectrum either continuously or in steps. It seemsthat in all the known electrostatic charged particle energy analysers,with the exception of the hyperbolic field analyser, the range ofenergies that can be analysed at any one time is small, the ratio of theenergy range to the mean energy being typically less than 0.1.Therefore, if the stepping method is used the required number of stepsis at least of the order of 10.

It is clearly advantageous to be able to analyse the whole energyspectrum simultaneously. The hyperbolic field analyser described by M.Jacka, M. Kirk, M. El Gomati and M. Prutton in Rev. Sci. Instrum, 70,2282 (1999) is able to do this. However, the hyperbolic field analyserhas a substantially planar geometry and so suffers from the drawbackthat it is only able to analyse charged particles incident over a narrowangular range is azimuth.

SUMMARY OF THE INVENTION

According to a first aspect of the invention there is provided a chargedparticle energy analyser for analysing charged particles having a rangeof energies comprising, electrostatic focusing means having alongitudinal axis, a charged particle source for directing chargedparticles into an electrostatic focusing field generated, in use, bysaid electrostatic focusing means, and detection means for detectingcharged particles focused by said electrostatic focusing means, whereinsaid electrostatic focusing field is defined by equipotentials whichextend about said longitudinal axis over a predetermined range isazimuth and charged particles having different energies are brought to afocus by the electrostatic focusing field at different respectivediscrete positions.

Charged particle energy analysers according to this aspect of theinvention have the capability to analyse simultaneously chargedparticles having a wide range of energies which are incident over theentire (360°) angular range in azimuth about the longitudinal axis orwhich are incident over one or more smaller azimuthal ranges. Thiscombination of features enables the energy spectra of charged particlesto be measured more rapidly than has been possible using knownanalysers, and also enables angular information to be obtained.

Charged particle energy analysers according to the invention may also beused in a second-order focusing mode whereby charged particles having arelatively narrow range of energies, but incident of a relatively wideangular range in elevation relative to the longitudinal axis can befocused.

According to another aspect of the invention there is provided a chargedparticle energy analyser for analysing charged particles comprising,electrostatic focusing means having a longitudinal axis, a chargedparticle source for directing charged particles into an electrostaticfocusing field generated, in use, by said electrostatic focusing means,and detection means for detecting charged particles focused by saidelectrostatic focusing means, wherein said electrostatic focusing meansis defined by equipotentials which extend about said longitudinal axisover a predetermined range in azimuth and said charged particle sourcedirects said charged particles into said electrostatic focusing fieldover a predetermined angular range in elevation relative to saidlongitudinal axis, said predetermined angular range in elevation and/orthe axial position of the charged particle source and/or the axialposition of the electrostatic focusing field being set or adjustable forsecond-order focusing of charged particles.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention are now described, by way of example only,with reference to the accompanying drawings, of which:

FIG. 1 is a schematic, longitudinal sectional view of a first embodimentof a charged particle energy analyser according to the invention,

FIG. 2 is an enlarged view of a part of the charged particle energyanalyser of FIG. 1 showing the contours of equipotentials in the rangefrom 0 to −3200 V, in steps of 200 V,

FIG. 3 is a schematic, longitudinal sectional view of a secondembodiment of a charged particle energy analyser according to theinvention,

FIG. 4 is a schematic, longitudinal sectional view of a third embodimentof a charged particle energy analyser according to the inventionoperating in a second-order, axis-to-surface focusing mode, and

FIG. 5 is a schematic, longitudinal sectional view of a fourthembodiment of a charged particle energy analyser according to theinvention operating in a second-order, axis-to-axis focusing mode,

FIG. 6 is a schematic longitudinal sectional view of a fifth embodimentof a charged particle energy analyser according to the invention,

FIG. 7 is an enlarged view of part of the charged particle energyanalyser of FIG. 6 showing the contours of equipotentials in the rangefrom −50 to −950 V in steps of 50 V,

FIG. 8 is a schematic longitudinal sectional view of a sixth embodimentof a charged particle energy analyser according to the invention,

FIG. 9 is an enlarged view of part of the charged particle energyanalyser of FIG. 8 showing the contours of equipotentials in the rangefrom −50 V to −800 V in steps of 50 V, and

FIG. 10 is a schematic longitudinal sectional view of a seventhembodiment of a charged particle energy analyser according to theinvention operating in a second-order focusing mode,

FIG. 11a shows a transverse cross-sectional view through an eighthembodiment of a charged particle energy analyser according to theinvention, and

FIG. 11b shows the contours of a number of equipotentials on a side wallof the analyser of FIG. 11a.

DESCRIPTION OF PREFERRED EMBODIMENTS

In the following description, the polarities of the applied potentialsare chosen for the analysis of negatively-charged particles, and in theembodiments of FIGS. 1 to 10 the charged particles are assumed to beelectrons. It will, of course, be appreciated that positively-chargedparticles may be analysed by reversing the polarities of the appliedpotentials.

Referring now to FIGS. 1 and 2 of the drawings, the charged particleenergy analyser has cylinder symmetry about a longitudinal axis z—z. Theanalyser comprises a localised source of electrons 1 situated on thataxis, an inner cylinder 2 of radius R₁ at ground potential, an outercylinder 3 of radius R₂=4R₁ whose ends have axial coordinates z=−3R₁ and15R₁ to which is applied a potential drop that varies linearly from+1039.7 V to −5198.6 V at the left- and right-hand ends respectively, afirst annular end disc 4 to which is applied a potential drop thatvaries from +1039.7 V at its outer edge to the ground potential at itsinner edge, a second annular disc 5 to which is applied a potential dropthat varies from −5198.6 V at its outer edge to the ground potential atits inner edge, and a detector 6 of electrons that forms a part of theouter surface of the inner cylinder 2 or conforms to a part of thatsurface. FIG. 1 also shows some representative curved trajectories 7 ofelectrons that originate at the localised source 1 and are focused ontothe detector 6 by the electrostatic focusing field created between theinner and outer cylinders 2,3. In this illustration, electrons havingthe initial energies 125, 200, 300, 500, 800, 1250, 2000 and 3000 eV arefocused at successive axial positions z₁, z₂ . . . z₈ in thelongitudinal direction.

In this example, the potentials applied to cylinders 2,3 are given byequation (1) below, where W=346.57 V (=2501n4). The potentials appliedto the annular end discs 4,5 are also given by equation (1) and arenon-linear. It can be seen from equation 1 that the equipotentialsbetween cylinders 2,3 vary monotonically (in this case linearly) in thelongitudinal direction and logorithmically in the radial direction.

In practice, the annular end discs 4,5 may be made from a material ofhigh electrical resistivity. Alternatively, instead of using a disc, therequired potential drop could be implemented using a plurality ofconcentric, annular rings each maintained at a different uniformpotential. The axial position of source 1 is z_(s)=1.85R₁, the medialelevational launch angle {overscore (θ)}_(s) of the electron beam B is0.472 rad (27.04°) relative to the longitudinal axis z—z and thehalf-angle of the beam is 0.016 rad (0.91°). The angular extent inelevation of the beam may be controlled by an aperture or aperturesprovided in a mask (not shown) located between the source 1 and theinner cylinder 2. The potential of the inner cylinder 2 is 0 V and, inthis embodiment, the beam is assumed to pass through a fine mesh or gridthat covers the entrance region of the inner cylinder 2.

The properties of the analyser are of course unchanged if the appliedpotentials and the energies are scaled linearly together.

As already described, the potential applied to the outer cylinder 3varies linearly from +1039.7 V at the left hand end to −5198.6 V at theright hand end. This linear variation in potential can be implemented bymeans of a cylinder 3 made from a material of high resistivity or,alternatively, the required potential may be simulated by means of aplurality of electrically conductive loops or rings, each of which ismaintained at a different uniform potential. The inner cylinder 2 whichis maintained at ground potential may be made from electricallyconductive material. The distribution of potential in the region betweencylinders 2,3 is uniform as a function of azimuthal angle about thelongitudinal axis z—z. The potential φ(r,z) can be expressed in terms ofthe radial and axial coordinates (r,z) by the expression:

φ(r,z)=−WzInr/1nR ₂   (1)

where z, r and R₂ are all expressed in units of R₁.

Because an analytical solution to the equations of motion in theelectrostatic field appear not to exist, the accurate CPO-2D programavailable on web site http://cpo.ph.man.uk has been used to solveLaplace's equation for various practical systems and to integrate theequations of motion to obtain particle trajectories.

Referring again to FIGS. 1 and 2, electrons emanating from source 1 onthe longitudinal axis z—z are focused on the surface of the innercylinder 2 after energy analysis and the electrons are detected there bya curved detector array 6 that conforms to or forms part of the surfaceof the inner cylinder 2.

As will be described in greater detail hereinafter, the electron beam Bspans a predetermined angular range in azimuth about the longitudinalaxis z—z. The angular range may be the entire (360°) azimuthal range orone or more smaller azimuthal ranges, and detector 6 may be so locatedand configured as to detect for electrons in one or more of theseangular ranges. Detector 6 may take the form of a microchannel arraydetector or a microsphere plate detector or a position-sensitiveresistive plate detector or any other suitable form of detector.

In a particular embodiment, the charged particle source 1 comprises atarget located on the longitudinal axis z—z and an irradiation devicefor directing radiation onto the target to generate charged particles.The irradiation device may, for example, be an electron gun and may belocated within the inner cylinder 2.

In practice, the trajectories of charged particles having the sameenergy but different elevational angles may be subject to dispersioncaused by their exposure to slightly differing field intensities in theregion between the inner and outer cylinders 2,3, and this reduces thesharpness of the focused image. However, the axial position z_(s) of thesource 1 and the medial, elevational launch angle {overscore (θ)}_(s) ofthe charged particle beam can be optimised to minimise the dispersiveeffect of the electrostatic field over the entire energy range ofinterest.

The axial position z_(i) of the image fonned by charged particles ofenergy E_(i) can be expressed as:

z _(i) =c ₀ +c ₂(θ_(s)−θ₀)² . . . ,   (2)

where c₀ is the axial position of the image if there is no dispersion,c₂ is a constant, θ₀ is the elevational launch angle needed to bring thecharged particles to a focus at the axial position c₀ when dispersion ispresent and θ_(s) is the launch angle of the trajectory of a chargedparticle within the beam.

The optimal condition exists when θ₀ is constant over the entire energyrange of interest and in the embodiment described with reference to FIG.1 this condition is almost satisfied when z_(s) is set at −1.85R₁. Table1 lists the resultant values of θ₀ and z_(i) obtained using this settingfor eight different energies, namely 125 eV, 200 eV, 300 eV, 500 eV, 800eV, 1250 eV, 2000 eV and 3000 eV. A suitable medial launch angle{overscore (θ)}_(s) is then 0.472 rad (27.04°).

As can be seen from this Table, the values of θ₀ are approximatelyconstant over the whole energy range, the slight inconstancy of θ₀ beingless than the typical range of angles accepted from a source.

A plot of exemplary trajectories is shown in FIG. 1, and these sametrajectories are shown in FIG. 2 on an enlarged scale together with thecontours of selected equipotentials.

Table 1 also includes values of the relative energy dispersionEdz_(i)/dE (normalised with respect to R₁) and a set of energyresolutions ΔE (normalised with respect to W), and these parameters arenow defined.

It will be apparent from equation 2 above that the spread Δz_(i) in theaxial position of an image at each energy E_(i) is given by theexpression:

Δz _(i) =|c ₂|(Δθ_(max))²   (3)

where Δθ_(max) is the maximum angular deviation of trajectories (in agiven range) from θ₀ for that energy. This spread in axial position isapproximately equivalent to an energy spreadΔE given by the expression:$\begin{matrix}{{{\Delta \quad E} = {0.5\Delta \quad {z_{f}/\frac{z}{E}}}},} & (4)\end{matrix}$

where the factor 0.5 is used as an approximation to convert the baseenergy width to the width at half height of a peak. As will be clearfrom the values of ΔE listed in the last column of Table 1, the usefulenergy range in this example covers at least a factor of 10.

For the source position z_(s) that has been used (−1.85R₁) θ₀ isstationary (in fact a maximum) when the initial energy E isapproximately 1000 eV. It might be useful in practice to change thevalue of E for which θ₀ is stationary by varying z_(s). This would givesome control over the dependence of ΔE on E. In practice, adjustments ofz_(s) may be facilitated by physically adjusting the axial position ofthe source 1 or by, in effect, axially translating the electrostaticfield relative to the source by changing the axial position at whichzero potential is applied to the outer cylinder.

Other parameters could be varied to make θ₀ more constant. In particularthe linear variation of the voltage on the outer cylinder could bereplaced by a slightly non-linear (but monotonic) variation, theparameters of which would be adjusted to minimise the fluctuations inθ₀. Alternatively, the shapes of the electrodes could be changed, forexample by using conically-shaped electrodes in place of discs andcylinders.

The analyser described with reference to FIGS. 1 and 2 generates anelectrostatic focusing field which is uniform as a function of azimuthalangle about the longitudinal axis. However, this need not necessarily bethe case; alternatively, the field may have n-fold rotational symmetryabout the longitudinal axis, where n is an integer. Such a field couldbe generated by replacing the inner cylinder with a tubular memberhaving n-fold symmetry, such as a flat-sided electrode having apolygonal transverse cross-section. This configuration has the advantagethat a detector can be readily located on one or more of the flat sides.

In another implementation of the invention, the outer cylinder isreplaced by a curved axially symmetric plate to which a (possiblyuniform) potential is applied and which is appropriately shaped tocreate equipotentials which vary monotonically in the longitudinaldirection, such as the linearly varying equipotentials generated by theinner and outer cylinders 2,3 of the embodiment described with referenceto FIGS. 1 and 2.

In the embodiment of FIG. 1, the inner cylinder 2 has a window orwindows by which electrons are admitted to the electrostatic focusingfield. The window or each window is so dimensioned and shaped as todefine a beam having required angular range in azimuth, and is coveredby a fine mesh or grid to help eliminate edge effects. The mesh could,for example, consist of a square array of holes or could be made fromparallel wires extending in the longitudinal z direction that arestretched across the window. The shielding properties of both thesetypes of mesh are known, as are the defocusing effects that the meshesproduce. The defocusing is effectively equivalent to increasing the sizeof the source.

Alternatively, the annular range in azimuth could be defined by anaperture or apertures provided in a mask (not shown) located between thesource 1 and the inner cylinder 2.

In some practical applications it might be more convenient to use anopen window, having the form of a slot in the azimuthal direction. Inanother embodiment shown in FIG. 3, electrons enter the electrostaticfocusing field through an open slot 7′ in the inner cylinder 2′extending between the axial coordinates z=0.05R₁ and 0.24R₁. The outercylinder 3′ has a radius of 3R₁ (in units of the radius of the innercylinder) and extends between the axial coordinates z=0 and z=10R₁. Aleft-hand end is closed by a disc at ground potential. As before, thepotentials applied to the outer cylinder and a right-hand end disc aregiven by equation (1), but where W=274.65 V (=2501n3). By application ofthe above-described analysis based on Equation 2 above, the optimalaxial position of the source 1′ is found to be −1.8R₁ and the optimalmedial elevational launch angle {overscore (θ)}_(s) is found to be 0.476rad (27.25°). The results of this analysis are shown in Table 2, andsome exemplary trajectories are illustrated in FIG. 3, where electronshaving the initial energies 125 eV, 200 eV, 300 eV, 800 eV, 1250 eV and2000 eV are focused at successive axial positions z₁, z₂ . . . z₆ in thelongitudinal direction. By comparing the data in Tables 1 and 2 it canbe seen that the values of θ₀ vary less when the entrance aperture isopen. This form of the analyser is however less suitable whensecond-order focusing is required, as will be discussed below.

Other positions of the electron source and the image are envisaged. Thesource and the image may both be located at the surface of the innercylinder 2 (surface-to-surface focusing) or, alternatively, the sourceand the image may both be located on the longitudinal axis z—z(axis-to-axis focusing). Alternatively, the source could be located in afield-free region between the longitudinal axis z—z and the innercylinder 2 and the image could also be located between the longitudinalaxis and the inner cylinder 2 or radially outwards of the innercylinder.

The source of electrons may, in effect, be a virtual source; in thiscase, the source directs electrons into the electrostatic focusing fieldfrom a location or locations offset from the longitudinal axis andincludes suitable focusing means, which could be in the form of one ormore conical lens, for example, for focusing electrons emitted from areal source (which may be located on-axis) at said location orlocations.

Similarly, such focusing means may be used to focus electrons forming animage onto one or more detector spaced apart from the image.

In another mode of operation, charged particle energy analysersaccording to the invention can be arranged to analyse charged particlesin a relatively narrow energy band incident over a relatively wideangular range in elevation.

One of the main advantages of a conventional Cylindrical Mirror Analyser(CMA), as described, for example, by J. S. Risley in Rev. Sci. Instrum.43, 95 (1972) is that it can be operated with second-order focusing.That is, it is possible to find conditions for which the axial positionz_(i) of the focus point has a dependence on the elevational launchangle θ_(s) of a charged particle of the form

z _(i) =c ₀ +c ₂(θ_(s)−θ₀)² +c ₃(θ_(s)−θ₀)³+ . . .   (5)

where the second-order term is zero. The absence of the usual quadraticterm implies that a wide range of angles θ_(s) can be accepted for agiven energy resolution of the analyser, provided that the coefficientc₃ is not too large.

FIG. 4 shows an embodiment of a charged particle energy analyseraccording to the invention operating in this second-order focusing mode.

Here, the dimensions of the analyser and the applied voltages areexactly the same as for the analyser described with reference to FIG. 3,but differs in that a fine mesh is placed across the entrance window inthe inner cylinder 2′ and in that the axial position z_(s) of the source1′ is 2R₁. It is found by analysis that the quadratic term in Equation 5becomes zero when E=854 eV and when the medial launch angle {overscore(θ)}_(s)=0.622 rad (35.6°). In this embodiment, the half angle of thebeam is 0.05 rad (2.86°).

In fact, a continuous spectrum of such conditions exists. For a givensource position z_(s) (within some range) it is possible to find valuesof E and {overscore (θ)}_(s) that give second-order axis-to-surfacefocusing. Some results are shown in Table 3.

Second-order focusing may also be performed in the axis-to-axis mode,and this is shown in FIG. 5. The dimensions of the analyser and theapplied voltages are exactly the same as the analyser described withreference to FIG. 4, but differs therefrom in that the axial positionz_(s) of the source is −R₁. Again, a fine mesh is placed across theentrance window in the inner cylinder 2′. It is found by analysis thatthe quadratic term in Equation 5 becomes zero when E=1345.5 eV and themedial elevational launch angle {overscore (θ)}_(s) of the beam is 0.444rad (25.46°). In this embodiment, the half angle of the beam is 0.05 rad(2.86°). Again a continuous spectrum of such conditions exists, as shownin Table 4.

As with the conventional CMA, a continuous spectrum of other modes ofoperation is possible and it is envisaged that second-order focusingmight also be achievable when the entrance window is open. It is alsopossible to find conditions for which the energy resolution is optimisedfor a particular narrow range of energies.

FIG. 6 of the drawings shows another embodiment of a charged particleenergy analyser according to the invention. As before, the polarities ofthe applied potentials are chosen for the analysis of negatively-chargedparticles, assumed to be electrons in this embodiment. However,positively-charged particles may be analysed by reversing the polaritiesof the applied potentials.

In contrast to the embodiments described with reference to FIGS. 1 to 3,the charged particle analyser of FIG. 6 is effective to focus electronshaving different energies E_(i) at different respective radial positionsr_(i) in a plane transverse to the longitudinal axis z—z. Thisarragement has the advantage that a flat detector, which may bedisc-shaped, can be used.

The analyser of FIG. 6 has substantially the same geometricalconfiguration as the analysers described with reference to FIGS. 1 to 3,comprising inner and outer cylinders 2″,3″ and a pair of annular enddiscs 4″,5″. As before, the potential φ(R₂,z) applied to the outercylinder 3″, where R₂ is the radius of the outer cylinder, varieslinearly as a function of the axial coordinate z according to theexpression:

φ(R ₂ ,z)=−Wz,

where z is expressed in units of the radius R₁ of the inner cylinder 2″.As before, the distribution of potential φ(r,z) between the cylinders2″,3″ can be expressed in terms of the radial and axial coordinate (r,z)by equation 1 above from which it can be seen that the equipotentialsbetween cylinders 2″,3″ vary monotonically (in this case linearly) inthe longitudinal direction and logarithmically in the radial direction.Again, the distribution of potential φ(r,z) is uniform as a function ofazimuthal angle about the longitudinal axis z—z.

In the case of the analysers described with reference to FIGS. 1 to 3,the medial elevational launch angle {overscore (θ)}_(s) of the electronbeam B relative to the longitudinal axis z—z is typically around 25°.However, in the case of the analyser of FIG. 6, the medial elevationallaunch angle {overscore (θ)}_(s) is much larger, and is typically around60°, although other angles in the range 50° to 70° say could be used.

As shown in FIG. 6, an electron beam B which enters the electrostaticfocusing field at a relatively large medial elevational launch angle{overscore (θ)}_(s) is deflected away from the longitudinal axis z—zand, in this embodiment, is brought to a focus in the plane of theleft-hand end disc 4″, where one or more flat detectors can bepositioned.

The electron beam B may span a predetermined angular range in azimutharound the longitudinal axis z—z, which may be the entire (360°)azimuthal range or one or more smaller azimuthal range. As before, therequired azimuthal range may be defined by one or more suitablydimensioned and shaped window in the inner cylinder 2″ and/or end disc4″ or by a mask or masks located between the source and the innercylinder.

For a given energy, electrons are brought to a focus on a respective arcor arcs in the focal plane and in the case of a beam spanning the entireazimuthal range the electrons are brought to a focus on a circle. One ormore suitable detectors would be so positioned and configured as todetect for focused electrons in the or each azimuthal range.

In this embodiment, the radius R₂ of the outer cylinder 3″ is 10R₁ andthe ends of the inner and outer cylinders have the axial coordinates z=0and z=3R₁. The value of W in equations 1 and 6 above is set at 333.3 Vand the potential applied to the inner cylinder 2″ and to the left-handend disc 4″ is set at 0 V, whereas the potential applied to the outercylinder 3″ varies linearly from 0 V at the left-hand end to −1000 V atthe right-hand end.

In this embodiment, the electron beam is produced by a localisedelectron source 1″ positioned on the longitudinal axis z—z in afield-free region at the axial position z_(s)=−0.6R₁.

FIG. 6 shows some representative curved trajectories of electrons thatare focused in the transverse plane of the left-hand end disc 4″. Inthis illustration, electrons having initial energies 40, 80, 160, 320and 640 eV are all approximately focused at successive radial positionsr₁,r₂,r₃,r₄,r₅ in the transverse focal plane. In this embodiment, themedial elevational launch angle of the electron beam B is 61.8° and thehalf-angle of the beam is 3.8°, and the beam enters the electrostaticfocusing field where the inner cylinder 2″ and the left-hand end disc 4″meet via a window in the form of an electrically conductive grid ormesh.

As already described, the potential applied to the outer cylinder 3″varies linearly from 0 V at the left hand end to −1000 V at the righthand end. This linear variation in potential can be implemented by meansof a cylinder 3″ made from a material of high electrical resistivityacross which the potential drop is applied. Alternatively, the requiredpotential may be simulated by means of a plurality of electricallyconductive loops or rings, each of which is maintained at a differentuniform potential. The inner cylinder 2″ which is maintained at groundpotential could be made from electrically conductive material.

The non-uniform potential on the right-hand disc 5″ may be created byapplying a potential drop across a disc made from a material of highelectrical resistivity. Alternatively, instead of using a disc therequired variation of potential could be simulated using a plurality ofconcentric rings each maintained at different uniform potential. Inanother alternative approach the required potential may be simulated inpiece-wise fashion using the afore-mentioned CPO-2D program by applyingthe required potential at a number (e.g. 30) positions on the disc thatare equally spaced radially and arranging for the potential to varylinearly between neighbouring positions.

FIG. 7 shows the trajectories of FIG. 6 on an enlarged scale and with adifferent aspect ratio, and also shows the contours of equipotentials inthe range −50 V to −950 V, in steps of 50 V.

It is apparent from FIG. 7 that lower energy electrons are brought to afocus slightly in front of a detector located in the plane of theleft-hand end disc 4″ whereas higher energy electrons are brought to afocus slightly behind the detector.

It has been found that the axial position z_(s) of the source does nothave any significant effect upon the quality of the focus obtained.However, significant improvements in the quality of the focus can beachieved by slightly modifying the potential distribution φ(r,z) definedby equation 1 above.

This can be accomplished empirically by optimising the potentialsapplied at selected positions on the inner and outer cylinders 2″,3″ andon the right-hand end disc 5″ while maintaining the left-hand end disc4″ at 0 V, and arranging for the potential between these selectedpositions to vary linearly as a function of axial and radial distancerespectively.

In this particular example, the selected positions on the right-hand enddisc 5″ have the radial coordinates r=1, 3, 6 and 9 and the selectedpositions on the inner and outer cylinders 2″,3″ have the axialcoordinates z=0, 1.5 and 3, where these coordinates are expressed inunits of R₁.

The radial and axial coordinates of the selected positions aresummarised in the first and second rows respectively of Table 5 and therespective voltages V₁, V₂ . . . V₇ applied at each selected positionare shown in the third row of the table. These voltages are also shownin FIG. 6.

The potential V₁ at the left-hand end of each cylinder is 0 V and it isfound to be desirable to fix the potential V₃ at the right-hand end ofthe outer cylinder 3″, at −1000 V in this example.

The remaining five potentials V₂, V₄, V₅, V₆ and V₇ are treated asvariables and are automatically adjusted using the aforementioned CPO-2Dprogram in the “automatic free-focus iteration” mode to optimize (i.e.minimise) the sizes of the focal points in the plane of the detector,while allowing the radial positions of the focal points to change.

The fourth row in Table 5 shows the voltage values that are derived fromequation 1 above, whereas the fifth row in the table shows the modifiedvalues optimised by empirical adjustment.

It will be appreciated that this optimisation procedure could also beapplied to the analysers described with reference to FIGS. 1 to 5.

FIG. 8 shows the electron trajectories obtained using the optimisedvoltage values. In this illustration the electrons have the initialenergies 40, 80, 160, and 320 eV which form a geometric progression witha multiplying factor of 2 and cover an energy range of 1:8. In this casethe medial elevational launch angle {overscore (θ)}_(s) is 60.8° and thehalf angle the beam is 2.05°. As before, the optimum axial position ofthe source is z_(s)=−0.6R₁.

FIG. 9 shows the trajectories of FIG. 8 on an enlarged scale and with adifferent aspect ratio, and also shows the contours of equipotentials inthe range −50 V to −800 V in steps of 50 V.

A comparison of FIGS. 7 and 9 clearly shows that much smaller focal spotsizes are attained using the empirically adjusted voltage values. Also,the contours of the equipotentials have a somewhat different shape.

Further improvements to the quality of the focus may be made byoptimising a larger number of voltages. Alternatively, or additionally,improvements may be made using different electrode shapes; for example,the outer cylinder 3″ could be replaced by an appropriately shapedcurved, axially symmetric plate to which a (possibly uniform) potentialis applied. Such a plate could also be used to generate a potentialdistribution φ(z,r) of the form defined by equation 1.

Alternatively, instead of modifying the potential distribution φ(z,r),the detector may be suitably shaped and positioned to conform to thesurface at which the electrons are focused. Furthermore, the electronsneed not be focused in the plane of the end disc, but could be focusedon some other transversely extending surface which could be in a fieldfree region beyond the end disc 4″ and need not necessarily be flat; thesurface could, for example, have a conical shape. The above-describedoptimisation procedure could be used to improve the quality of the focusat a desired surface.

By analogy to equation 2 above, the radial position r_(i) at which thetrajectory of an electron of energy E_(i) intersects the focal plane canbe expressed as:

r _(i) =c ₀ +c ₂(θ_(s)−θ₀)²+ . . .

where c₀ and c₂ are coefficients which are a function of energy, θ_(s)is the elevational launch angle of an electron in the beam and θ₀ is theelevational launch angle needed to bring the electron to a focus whenenergy dispersion is present. For values of θ_(s) near to θ₀ afirst-order focus exists at r_(i)=c₀.

Table 6 summarises the values of θ₀, r_(i) and c₂ obtained using theanalyser of FIG. 8 for electrons having the energies 56.6, 80, 113.1,160, 226.3, 320, 452.5 and 640 eV and for a source having the axialposition z_(s)=−0.6R₁. Also shown in Table 6 are computed values ofrelative energy dispersion Edr_(i)/dE and the dimensionless figure ofmerit g₂, given by the expression:

g ₂ =c ₂ ⁻¹ Edr _(i) /dE.

The values of r_(i), c₂ and Edr_(i)/dE in this table are expressed inunits of R₁.

The optimum condition exists when θ₀ is constant over the entire energyrange and it can be seen from the values of θ₀ listed in Table 6 thatthis condition is almost satisfied. The variation in the values of θ₀ isless than the typical half angle of the beam, and this variation is evensmaller over a narrower energy range. The variation is particularlysmall (0.2°) in the energy range from approximately 100 eV to 450 eV.

As shown in Table 6, the values of θ₀ decrease monotonically as energy Eincreases. This behaviour can be altered by changing the axial positionof the source. For example, a shallow minimum in θ₀ exists when theaxial source position z_(s)=−0.7R_(i) (i.e. θ₀=1.081, 1.069, and 1.071at energies E=80, 226 and 640 eV respectively). However, in this case,the coefficient c₂ is too small to allow a maximum in r_(i) at energiesE<80 eV, but there is approximate second-order focusing at these energyvalues and so the focal spot size is still relatively small. Therefore,there may be some benefit in adjusting the source position, but inpractice the optimum position will depend on the application to whichthe analyser is being put.

For a source position z_(s)=−0.6R_(i), the values of r_(i) can beapproximately parametrized by the expression:

lnr _(i) =a+blnE+c(lnE)²,

where the constants a,b and c are 0.02353, 0.06433 and 0.03643respectively.

The charged particle energy analysers described with reference to FIGS.6 to 9 can also operate in the second order focusing mode whereby arelatively narrow band of energies can be analysed with improved energyresolution.

Second order focusing occurs when the quadratic term in equation 7 aboveis zero, and in this condition the radial position r_(i) at which thetrajectory of an electron intersects the focal plane can be expressedas:

r _(i) =c ₀ +c ₃(θ_(s)−θ₀)³⁺ . . . ,

where the coefficients c₀ and c₃ depend on energy. In this situation,the angular range in elevation that can be accepted is larger for agiven energy resolution.

FIG. 10 shows an analyser operating in the second-order focusing mode.The geometrical configuration of the analyser and the applied potentialsare exactly as described with reference to FIG. 8; however, the axialposition of the source is set at z_(s)=−0.8R₁. It is found that thequadratic term becomes zero, and second-order focusing takes place, whenthe energy E=97.02 eV and the elevational launch angle θ₀=62.6°. In theanalyser of FIG. 10, the medial elevational launch angle {overscore(θ)}_(s) of the electron beam is 62.2°, the half angle of the beam is3.7° and the beam enters the electrostatic field region via a window inthe left-hand end disc 2″ in the form of an electrically conductive gridor mesh.

A contiuous spectrum of the conditions for second-order focusing exists.Thus, for a given source position z_(s) (within some limited range) itis possible to find values of E and θ₀ that satisfy the conditions forsecond-order focusing and some values are listed in Table 7. Also shownin this table are values of the relative energy dispersion Edr_(i)/dEand the figure of merit g₂.

It can be seen from Table 7 that when the source positions z_(s)=−0.6R₁,second order focusing takes place when the energy is 38.4 eV which isjust below the lower energy limit (40 eV) of the analysers describedwith reference to FIGS. 6 to 8 when operating in the ‘wide-energy’ firstorder focusing mode illustrated in those Figures.

Accordingly, in this situation, where the axial source position isfixed, it is possible to use the first order, ‘wide-energy’ focusingmode in combination with the second-order focusing mode.

Initially, the first order, wide-energy focusing mode would be used toproduce a relatively wide energy spectrum of the charged particles inthe beam, and the applied potentials would then be scaled appropriatelyto produce high-resolution, second-order focusing in a selected narrowenergy range in the spectrum.

As will be clear from Table 7, second order focusing occurs atrelatively small values of r_(i). Accordingly, when the first and secondorder modes of operation are used in combination the inner radial partof the analyser would be used predominantly for second order focusingwhereas the outer parts of the detector would only be used forwide-energy, first-order focusing as shown in FIGS. 6 and 8.

In the embodiments described with reference to FIGS. 1 to 10, the innerand outer field defining elements extend over the entire (360°) angularrange in azimuth around the longitudinal axis z—z.

However, alternatively, the inner and outer field defining elements mayextend over a smaller azimuthal range. An example of this is shown inFIG. 11a. This figure shows a transverse cross-sectional view throughinner and outer field defining elements 2″′,3″′ in the form ofcylindrical segments subtending an angle ψ at the longitudinal axis,which in this example is about 60°. The arcuate end edges of thecylindrical segments are joined by end walls in the form of annularsectors and the longitudinally extending side edges of the cylindricalsegments are joined by flat side walls S₁, S₂.

The electrostatic focusing field created within this structure may haveexactly the same form as that described with reference to FIGS. 1 to 10provided the potential distribution at the side walls is correct (asdefined by Equation 1 above, for example). The required potentialdistribution can be achieved in a variety of different ways. Forexample, the side walls may be made from a material of high electricalresistivity and the required potentials are applied at different pointsalong the edges of the side walls.

Alternatively, the side walls may be made from electrically insulatingmaterial on the surface of which is deposited a series of electricallyconductive lines or strips which are shaped to conform to the contoursof the equipotentials intersecting the side walls, and to each of whichis applied the required potential. This is illustrated in FIG. 11b.

In a yet further alternative approach, instead of using an electricallyinsulating substrate the electrically conductive lines or strips may beself-supporting. It will be appreciated that the field defining elementsdescribed with reference to any of FIGS. 1 to 10 can be modified for useover a relatively narrow angular range in azimuth in the mannerdescribed with reference to FIG. 11, for example.

TABLE 1 E θ₀ Z_(i)/R₁ Edz_(i)/dE ΔE 125 0.4674 1.455 0.855 0.22 2000.4691 1.876 1.102 0.23 300 0.4703 2.349 1.380 0.23 500 0.4715 3.1401.845 0.24 800 0.4722 4.136 2.430 0.37 1250 0.4719 5.416 3.182 0.51 20000.4704 7.262 4.267 1.41 3000 0.4679 9.429 5.540 4.34

TABLE 2 E θ₀ z₁/R₁ Edz₁/dE 125 0.4760 1.46 0.780 200 0.4758 1.882 1.028300 0.4762 2.354 1.318 500 0.4766 3.146 1.812 800 0.4766 4.142 2.4601250 0.4758 5.422 3.329 2000 0.4740 7.267 4.622

TABLE 3 z₅/R₁ E θ₀ z_(i)/R₁ −2 43.5 0.435 1.136 −1.5 123 0.471 1.483 −1201 0.519 2.001 0 410 0.574 3.144 1 630 0.606 4.230 2 854 0.622 5.287 31082 0.635 6.328 4 1315 0.642 7.367

TABLE 4 z₅/R₁ E θ₀ z_(i)/R₁ −2.5 1206 0.359 5.886 −2.0 1223 0.386 5.988−1.0 1356 0.441 6.448 0.0 1556 0.494 7.102 1.0 1763 0.538 7.807 2.0 20090.573 8.630 3.0 2281 0.598 9.471 5.0 2862 0.631 11.35

TABLE 5 r 1 10 10 10 6 3 1 1 z 0 0 1.5 3 3 3 3 1.5 V V₁ V₁ V₂ V₃ V₄ V₅V₆ V₇ Eqn(2) 0 0 −500 −1000 −778 −477 0 0 Emp 0 0 −291 −1000 −869 −45569 −31

TABLE 6 E θ₀ r_(i) c₂ Edr_(i)/dE g₂ 56.6 1.0825 2.403 −5.51 0.861 0.15680 1.0744 2.731 −7.61 1.048 0.138 113.1 1.0711 3.134 −10.12 1.281 0.127160 1.0700 3.629 −12.92 1.575 0.122 226.3 1.0698 4.236 −16.15 1.9460.121 320 1.0695 4.985 −19.73 2.416 0.123 452.5 1.0682 5.919 −23.693.018 0.127 640 1.0653 7.103 −28.49 3.801 0.133

TABLE 7 Z₅ E θ₀ r₁ c₃ Edr_(i)/dE g₃ −0.6 38.4 1.112 2.173 55.1 0.6430.012 −0.7 66.5 1.104 2.657 44.0 0.915 0.021 −0.8 97.0 1.093 3.106 41.11.151 0.028 −0.9 133.3 1.089 3.571 38.4 1.392 0.036 −1.0 172.6 1.0874.025 38.5 3.178 0.083

What is claimed is:
 1. A charged particle energy analyser arranged toanalyze charged particles having a range of energies, comprising:electrostatic focusing means including inner and outer field definingmeans extending about an axis of the electrostatic focusing means over apredetermined range in azimuth, a charged particle source for directingsaid charged particles into an electrostatic focusing field generated,in use, by said electrostatic focusing means between said inner andouter field defining means, and detection means positioned to receiveand detect charged particles focused by said electrostatic focusingmeans, wherein said electrostatic focusing field is defined byequipotentials which extend about said axis and which vary substantiallylinearly in the direction of said axis and which vary substantiallylogarithmically in the radial direction orthogonal to said axis, wherebycharged particles having different energies are brought to a focus bythe electrostatic focusing field at different discrete positions on asurface of the detection means.
 2. An analyser as claimed in claim 1wherein said surface of said detection means is transverse to said axis.3. An analyser as claimed in claim 2 wherein said surface is orthogonalto said axis.
 4. An analyser as claimed in claim 2 wherein said surfaceis planar.
 5. An analyser as claimed in claim 2 wherein said surface iscurved.
 6. An analyser as claimed in claim 5 wherein said surface isconical.
 7. An analyser as claimed in claim 2 wherein said surface is ina field-free region beyond the electrostatic focusing field.
 8. Ananalyser as claimed in claim 1 wherein said charged particles havingdifferent energies are brought to a focus by the electrostatic focusingfield at different discrete positions that are spaced apart from eachother in the axial direction.
 9. A charged particle energy analyser asclaimed in claim 1 wherein said charged particle source directs saidcharged particles into said electrostatic focusing field over apredetermined angular range in elevation relative to said axis, and saidpredetermined angular range in elevation and/or the axial position ofthe charged particle source and/or the axial position of theelectrostatic focusing field are set or adjustable for second-orderfocusing of the charged particles.
 10. An analyser as claimed in claim 1wherein said equipotentials are symmetrical about said axis.
 11. Ananalyser as claimed in claim 1 wherein said outer field defining meansis maintained, in use, at a potential relative to said inner fielddefining means.
 12. An analyser as claimed in claim 1 wherein said innerfield defining means and said outer field defining means comprise aninner cylinder and an outer cylinder respectively, wherein said innercylinder is maintained, in use, at a uniform potential and said outercylinder is maintained, in use, at potential varying monotonically inthe axial direction.
 13. An analyser as claimed in claim 12 wherein saidpotential varies linearly in the axial direction.
 14. An analyser asclaimed in claim 13 wherein said outer cylinder is made fromelectrically resistive material.
 15. An analyser as claimed in claim 11wherein said outer field defining means comprises a plurality ofdiscrete field defining elements, each said element being maintained, inuse, at a different respective potential with respect to said innerfield defining means.
 16. An analyser as claimed in claim 15 whereineach said field defining element has the form of a ring or hoop.
 17. Ananalyser as claimed in claim 15 wherein each said field defining elementhas the form of a hollow, truncated cone.
 18. An analyser as claimed inclaim 11 wherein said outer field defining means comprises a pluralityof discrete field defining elements each being made from electricallyresistive material and being maintained, in use, at a respectivepotential which increases monotonically in the axial direction.
 19. Ananalyser as claimed in claim 18 wherein each said element has the formof a cylinder.
 20. An analyser as claimed in claim 18 wherein each saidelement has the form of a hollow, truncated cone.
 21. An analyser asclaimed in claim 1 including first and second end elements located atopposite ends of said inner and outer field defining means in respectiveplanes orthogonal to said axis, each of said first and second endelements being maintained in use at a potential relative to said innerfield defining means which varies logarithmically in the radialdirection.
 22. An analyser as claimed in claim 21 wherein each said endelement is made from electrically resistive material.
 23. An analyser asclaimed in claim 21 wherein each said end element comprises a pluralityof concentric electrically conductive rings each being maintained, inuse, at a different respective potential.
 24. An analyser as claimed inclaim 21 wherein charged particles having different energies are broughtto a focus by the electrostatic focusing field at different respectivediscrete positions in the plane of one of said first and second endelements.
 25. An analyser as claimed in claim 1 wherein saidelectrostatic focusing means is so configured that the distribution ofpotential in said electrostatic focusing field is uniform as a functionof azimuthal angle about said axis.
 26. An analyser as claimed in claim1 wherein said electrostatic focusing means is so configured that thedistribution of potential in said electrostatic focusing field hasn-fold rotational symmetry about said axis, where n is an integer. 27.An analyser as claimed in claim 11 wherein said inner field definingmeans and/or said outer field defining means has n-fold rotationalsymmetry about said axis, where n is an integer.
 28. An analyser asclaimed in claim 27 wherein said inner field defining means comprises aplurality of flat side surfaces having n-fold rotational symmetry aboutsaid axis, where n is the number of said surfaces.
 29. An analyser asclaimed in claim 28 wherein said charged particles are brought to afocus at discrete positions spaced apart from each other along one ormore of said side surfaces and said surface of said detection means islocated at said one or more side surfaces to detect the focused chargedparticles.
 30. An analyser as claimed in claim 1 wherein said chargedparticles are brought to a focus at discrete positions spaced apart fromeach other along said inner field defining means and said surface ofsaid detection means is located at and conforms to said inner fielddefining means to detect the focused charged particles.
 31. An analyseras claimed in claim 1 wherein said charged particles are brought to afocus at said axis and said surface of said detection means is locatedon said axis to detect the focused charged particles.
 32. An analyser asclaimed in claim 1 wherein said charged particle source is located onsaid axis.
 33. An analyser as claimed in claim 32 wherein said chargedparticle source comprises a target located on said axis and means fordirecting radiation onto said target whereby to generate said chargedparticles.
 34. An analyser as claimed in claim 1 wherein said chargedparticle source comprises a target located on said axis and means fordirecting radiation onto said target whereby to generate said chargedparticles, said target and said means for directing radiation beinglocated within said inner field defining means.
 35. An analyser asclaimed in claim 33 wherein said means for directing radiation is anelectron gun.
 36. An analyser as claimed in claim 1 wherein said chargedparticle source directs charged particles into said electrostaticfocusing field over a predetermined angular range in azimuth about saidaxis.
 37. An analyser as claimed in claim 36 wherein said chargedparticle source directs said charged particles into said electrostaticfocusing field over the entire (360°) angular range in azimuth.
 38. Ananalyser as claimed in claim 1 wherein said charged particle sourcedirects charged particles into said electrostatic focusing field overtwo or more discrete angular ranges in azimuth about said axis.
 39. Ananalyser as claimed in claim 1 wherein said charged particle sourcedirects charged particles into said electrostatic focusing field overone or more predetermined angular range in azimuth about said axis, saidcharged particles being admitted to the electrostatic focusing field byone or more windows in the inner field defining means.
 40. An analyseras claimed in claim 39 wherein the or each said window has the form ofan electrically conductive grid or mesh.
 41. An analyser as claimed inclaim 1 wherein said charged particle source directs charged particlesinto said electrostatic focusing field over two or more predeterminedangular range in azimuth about said axis, and said detection means is soconfigured and arranged as to detect charged particles derived from eachsaid angular range.
 42. An analyser as claimed in claim 1 wherein saiddetection means comprises one or more detector selected from a multichannel array detector, a microsphere array detector and aposition-sensitive resistive plate detector.
 43. An analyser as claimedin claim 42 wherein said one or more detector incorporates aphosphor-coated detection plate.
 44. An analyser as claimed in claim 1including means for adjusting the axial position of said chargedparticle source.
 45. An analyser as claimed in claim 11 including meansfor adjusting said potential whereby to vary the axial position of theelectrostatic focusing field relative to said charged particle source.46. An analyser as claimed in claim 1 wherein said charged particlesource includes aperture means for directing charged particles into saidelectrostatic focusing field over a predetermined angular range inelevation relative to said axis.
 47. An analyser as claimed in claim 46wherein said predetermined angular range in elevation and/or the axialposition of said charged particle source and/or the axial position ofthe electrostatic focusing field are set or adjustable for second-orderfocusing of charged particles.
 48. An analyser as claimed in claim 1wherein said charged particle source directs said charged particles froma location or locations offset from said axis.
 49. An analyser asclaimed in claim 48 wherein said charged particle source includes meansfor focusing charged particles at said location or locations.
 50. Ananalyser as claimed in claim 1 wherein said charged particle source andsaid detection means are both located between said axis and said innerfield defining means.
 51. An analyser as claimed in claim 1 wherein saidcharged particles are brought to a focus at discrete positions spacedapart from each other along said inner field defining means and saiddetection means comprises a detector located radially inwards orradially outwards of the inner field defining means and means forfocusing said focused charged particles onto said surface of saiddetector.
 52. An analyser as claimed in claim 1 wherein said chargedparticle source includes a real source located at a first position andmeans for focusing charged particles produced by said real source at asecond position different from said first position whereby said chargedparticle source creates a virtual source at said second position fromwhere said charged particles are directed into said electrostaticfocusing field.
 53. An analyser as claimed in claim 1 wherein said outerfield defining means comprises a curved plate having rotational symmetryabout said axis.
 54. An analyser as claimed in claim 53 wherein saidcurved plate is maintained at a uniform potential.
 55. An analyser asclaimed in claim 24 wherein said one of said first or second endelements is maintained at zero potential.
 56. A method for operating acharged particle energy analyser as claimed in claim 1 comprising thesteps of applying voltage to said electrostatic focusing means in orderto obtain operation in the first-order focusing mode within apredetermined energy range and scaling the applied voltage in order toobtain operation in the second-order focusing mode at a selectednarrower energy range within said predetermined energy range.
 57. Ananalyser as claimed in claim 1 wherein said predetermined range inazimuth is the entire (360°) azimuthal range.
 58. An analyser as claimedin claim 1 wherein said inner and outer field defining means comprisesan inner cylindrical segment and an outer cylindrical segmentrespectively, wherein said inner and outer cylindrical segments extendover a predetermined angular range in azimuth and said outer cylindricalsegment is maintained, in use, at a potential varying linearly in theaxial direction.
 59. An analyser as claimed in claim 58 wherein thelongitudinal side edges of the inner and outer cylindrical segments arejoined by side walls.
 60. An analyser as claimed in claim 59 whereinsaid side walls are adapted to define a predetermined potentialdistribution over their inward facing surfaces.